What is the complete factorization of the polynomial below

Mathematics

1 answer:

DerKrebs [107]2 years ago

7 0

Answer:

$a. \ (x-2)(x+i)(x-i)$

Step-by-step explanation:

First of all let's notice that $(x-i)(x-i)=(x-i)^2 = x^2+2xi-1 \in \mathbb{C}$ while our original polynomial is real. So we can rule out the even options B and D. At this point, if the polynomial has a factor of $(x-\alpha)$ it means tha $\alpha$ is a zero of the polynomial. Let's check both 2 (for option a) and -2 (for option c)

$p(2)=2^3-2(2)^2+2-2= 8-8+2-2=0$

$p(-2)= (-2)^3-2(-2)^2+(-2)-2=-8-8-2-2=-20$

At this point 2 is a zero, and our final factoring is a $(x-2)(x+i)(x-i)$

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PLEASE HELP !!!!!!! Jordan got a new money bank for his birthday with $20 inside. He puts part of his weekly allowance in his ba

kupik [55]

Answer:

Slope of the function is $=3.75$ ,Y-intercept $=20$ .

The function is $y=3.75(x)+20$ with initial value $=20$ ,Jordan puts $\$3.75$ each week andthe amount saved by Jordan after $52$ week $=215\$$ .

Step-by-step explanation:

To understand the slope and y-intercept lets assign $x$ as number of weeks and $y$ as the money saved by Jordan.

Jordan is already having a sum of $\$20$ inside the money bank so in $0$ week the amount is $\$20$ can be written as $(x,y) =(0,20)$ in coordinate form.

SImilarly

We have $(x,y) =(0,20)$ and $(x_1,y_1) =(25,113.75)$

Part A:

The function is $y=m(x)+b$

From point-slope form,we have slope (m)

and $m=\frac{y_1-y}{x_1-x}$ ,plugging the values of the points.

$m=\frac{113.75-20}{25-0}=3.75$

Y-intercept of this function is the constant term or the money of $\$20$ that is already inside the money bank.

We can also calculate y-intercept by arranging the function as $b=y-m(x)$ choosing any $(x_1,y_1) = (25,113.75)$ coordinate and here $b$ is the y-intercept.